The use of a hollow metal sleeve or cannula in combination with an obturator (which may be referred to as a stilette or stylet), this combination being sometimes referred to as a trocar, is widely used in medicine for obtaining biopsy specimens. The obturator has a sharp point, and when the obturator is within the cannula, the obturator enables the combination to be inserted into the body. If the obturator is then removed, a biopsy specimen can be obtained within the cannula. U.S. Pat. No. 6,890,308 (Islam) describes a bone marrow biopsy needle of this general type, which comprises a hollow tube or hollow needle in conjunction with a trocar needle or stilette, i.e. an obturator. The hollow needle is mostly of constant internal and external diameter, but has sharp facets to form a cutting edge at its front end, and a front end portion of the hollow needle is of reduced diameter, this front end portion being formed by swaging so there is a frusto-conical transition in which the bore is tapered. If the hollow needle is pushed for example into bone marrow, without the obturator, then a sample of the marrow containing bone will go into the hollow needle; the front end portion of reduced diameter tends to grip the resulting sample, so the sample remains within the needle when the needle is withdrawn. This biopsy needle is quite effective, but an improved biopsy needle would be advantageous.